Section Modulus calculation and optimization
In this Challenge I learned how to find Section Inertia Analysis for the Hood Assembly which is done in the previous Challenge.
Section Modules:
It is the ratio of area moment of inertia about the Neutral Axis and to the distance of Outermost fiber from the Neutal Axis. The Neutral Axis is the layer in a particular Cross Section where there will be either Tension nor Compression.
Section Modules Formula:
Z=I/Y mm^3
Z= Section Modulus
I=Area Moment of Inertia
Y=Distance from Neutral Axis to the Outermost Fiber
Now we need to find the Y value which is the distance from the center of the Hood Assembly to the outer end of the Fiber.
Fig 1. Intersection Curve
Fig 2. Distance Value of Y from Neutral Axis 1
The distance is 439.9996mm but i have taken it as 440mm. Then the Section Inertia Analysis is done.
Fig 3. Section Inertia Analysis 1
From the above the data the Moment of Inertia Minimum and Maximum value is taken.
MOI Min: 2.939694972*10^5 mm^4
MOI Max: 9.004050364*10^7 mm^4
Y=440mm
Now lets solve it in the given formula,
MOI Min Z=Imin/Y mm^3
Z=2.939694972*10^5/440 =668.11243636 mm^3
MOI Max Z=Imax/Y mm^3
Z=9.004050364*10^7/440 =204637.50827272 mm^3
Now the bottom surface area is offseted 0.5mm downward and the gap inbetween the area are joined using line tool. The Offset is done to increase the Moment of Inertia.
After the changes is done the Section Inertia Analysis is done and the result is given below.
Fig 4. Section Inertia Analysis 2
As we expected their is a change in the values, lets check them in the equation to find the difference.
From the above data we take the moment of Inertia value,
MOI Min:3.070628708*10^5 mm^4
MOI Max: 8.998683671*10^7 mm^4
Y will be same as 440mm
Lets solve it in the given formula,
Z=I/Y mm^3
MOI Min Z=Imin/Y mm^3
Z=3.070628708*10^5/440 =697.87016090909 mm^3
MOI Max Z=Imax/Y mm^3
Z=8.998683671*10^7/440 = 204515.53797727 mm^3
Now we can get a conclusion that from the Section Inertia Analysis value the Section Inertia 1 MOI Min is lesser than the Section Inertia 2 MOI Min. The difference between them is 29.7577mm.
Whereas in the Max Section value in the Section Inertia 1 MOI Max is greater than the Section Inertia 2 MOI Max. The difference between then is 121.97mm.
So for the Inertia Minimum Value the Section Inertia Analysis 2 is better. Then for the Inertia Maximum Value the Section Inertia Analysis 1 is better.